{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T10:12:24Z","timestamp":1784110344987,"version":"3.55.0"},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2011,3,9]],"date-time":"2011-03-09T00:00:00Z","timestamp":1299628800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2011,7]]},"abstract":"<jats:p>Two players share a connected graph with non-negative weights on the vertices. They alternately take the vertices (one in each turn) and collect their weights. The rule they have to obey is that the remaining part of the graph must be connected after each move. We conjecture that the first player can get at least half of the weight of any tree with an even number of vertices. We provide a strategy for the first player to get at least 1\/4 of an even tree. Moreover, we confirm the conjecture for subdivided stars. The parity condition is necessary: Alice gets nothing on a three-vertex path with all the weight at the middle. We suspect a kind of general parity phenomenon, namely, that the first player can gather a substantial portion of the weight of any \u2018simple enough\u2019 graph with an even number of vertices.<\/jats:p>","DOI":"10.1017\/s0963548311000071","type":"journal-article","created":{"date-parts":[[2011,3,9]],"date-time":"2011-03-09T04:48:50Z","timestamp":1299646130000},"page":"623-629","source":"Crossref","is-referenced-by-count":21,"title":["A Graph-Grabbing Game"],"prefix":"10.1017","volume":"20","author":[{"given":"PIOTR","family":"MICEK","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"BARTOSZ","family":"WALCZAK","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2011,3,9]]},"reference":[{"key":"S0963548311000071_ref3","unstructured":"[3] Knauer K. , Micek P. and Ueckerdt T. How to eat $\\frac{4}{9}$ of a pizza. Discrete Mathematics, to appear."},{"key":"S0963548311000071_ref4","unstructured":"[4] Micek P. and Walczak B. Parity in graph sharing games. Submitted."},{"key":"S0963548311000071_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13562-0_31"},{"key":"S0963548311000071_ref7","volume-title":"Mathematical Puzzles: A Connoisseur's Collection","author":"Winkler","year":"2004"},{"key":"S0963548311000071_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-10217-2_35"},{"key":"S0963548311000071_ref6","unstructured":"[6] Winkler P. M. (2008) Problem posed at Building Bridges, a conference in honour of the 60th birthday of L\u00e1szl\u00f3 Lov\u00e1sz, Budapest."},{"key":"S0963548311000071_ref5","unstructured":"[5] Rosenfeld M. A gold-grabbing game. Open Problem Garden: http:\/\/garden.irmacs.sfu.ca\/?q=op\/a_gold_grabbing_game."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548311000071","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T03:57:24Z","timestamp":1556337444000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548311000071\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,9]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2011,7]]}},"alternative-id":["S0963548311000071"],"URL":"https:\/\/doi.org\/10.1017\/s0963548311000071","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3,9]]}}}